Rewrite as a simplified fraction. ${2.\overline{90} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 290.909...\\ 1x &= 2.909...\end{align*}}$ Subtracting the two equations, we have: ${99x = 288}$ ${x = \dfrac{288}{99}} $ ${x = \dfrac{32}{11}} \text{or} {2 \dfrac{10}{11}}$